Which condition is characterized by a unilateral drooping of the pupil and ptosis?

The condition characterized by a unilateral drooping of the pupil and ptosis is Horner's syndrome. Horner's syndrome occurs due to the disruption of sympathetic nerve pathways that innervate the eye. This leads to symptoms that include ptosis (drooping of the eyelid), miosis (constricted pupil), and anhidrosis (lack of sweating) on the affected side of the face.

In contrast, oculomotor nerve palsy typically results in a fixed, dilated pupil and often associated with an eye that is stuck in a down and out position, rather than just a drooping pupil. Accommodation paralysis is related to the inability to change the shape of the lens for focusing, leading to blurred vision but not typically associated with drooping structures. Diplopia refers to double vision and does not encompass the specific signs of ptosis and pupil changes seen in Horner's syndrome.

Thus, Horner's syndrome stands out as the correct answer due to its specific combination of symptoms related to unilateral drooping of the pupil and eyelid.